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Mathematics - Analysis | Mastering the Discrete Fourier Transform in One, Two or Several Dimensions - Pitfalls and Artifacts

Mastering the Discrete Fourier Transform in One, Two or Several Dimensions

Pitfalls and Artifacts

Amidror, Isaac

2013, XII, 375 p.

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  • Written in an informal style using a pictorial, intuitive approach rather than a rigorous mathematical treatment, intentionally avoiding a purist's approach based on theorems and proofs
  • Teaches how to correctly interpret the DFT results, and how to distinguish between true spectral contents and the various artifacts that are only due to DFT
  • Contains information on subjects rarely covered in literature, such as practical questions regarding the correct interpretation of the DFT results

The discrete Fourier transform (DFT) is an extremely useful tool that finds application in many different disciplines. However, its use requires caution. The aim of this book is to explain the DFT and its various artifacts and pitfalls and to show how to avoid these (whenever possible), or at least how to recognize them in order to avoid misinterpretations. This concentrated treatment of the DFT artifacts and pitfalls in a single volume is, indeed, new, and it makes this book a valuable source of information for the widest possible range of DFT users. Special attention is given to the one and two dimensional cases due to their particular importance, but the discussion covers the general multidimensional case, too. The book favours a pictorial, intuitive approach which is supported by mathematics, and the discussion is accompanied by a large number of figures and illustrative examples, some of which are visually attractive and even spectacular.

 

Mastering the Discrete Fourier Transform in One, Two or Several Dimensions is intended for scientists, engineers, students and any readers who wish to widen their knowledge of the DFT and its practical use. This book will also be very useful for ‘naive’ users from various scientific or technical disciplines who have to use the DFT for their respective applications. The prerequisite mathematical background is limited to an elementary familiarity with calculus and with the continuous and discrete Fourier theory.

Content Level » Research

Keywords » 2D DFT - Aliasing - DFT - DFT Artifacts - Discrete Fourier Transform - Fourier Analysis - Leakage - Multidimensional DFT

Related subjects » Analysis - Computational Science & Engineering - Mathematics Education - Theoretical Computer Science

Table of contents 

Introduction.- Background and basic notions.- Data reorganizations for the DFT and the IDFT.- True units along the axes when plotting the DFT.- Issues related to aliasing.- Issues related to leakage.- Issues related to resolution and range.- Miscellaneous issues.- Appendices.

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